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## DESIGN, ANALYSIS AND EXPERIMENTAL VERIFICATION OF A NOVEL NONLINEAR PI CONTROLLER

#### Ali Fuat Ergenc [1] , Handan Nak [2] , Şirin Akkaya [3]

##### 237 832

In this study, a novel variable gain PI controller structure is introduced. The proposed controller structure consists of a sector-bounded nonlinear function of the relative error value in cascade with a linear fixed-gain PI controller. The stability analysis of the closed loop system is examined through Popov stability criterion, Routh-Hurwitz stability method and stability boundary locus method for both second-order and higher-order systems. In addition, the performance of the controller against parameter variations and disturbances is investigated through some simulations for second order systems.  An experimental study, an active suspension system, is conducted to examine the performance of the controller for higher order systems. In the literature, there are similar controllers, but the proposed one is superb in terms of effectiveness and stability. The new controller prevents the saturation of the controller signal. Simulation results and experimental studies reveal that proposed controller structure is quite effective for both lower and higher order systems.

: Nonlinear PI, Variable gain, Popov criterion, stability boundary locus, Active suspension
• [1] Ang K, Chong G, Li Y. PID control system analysis, design, and technology, IEEE Trans. Control Syst. Technol., vol. 13, no. 4, pp. 559–576, Jul. 2005.
• [2] Lau K, Middleton R. Switched integrator control schemes for integrating plants, in Proc. Eur. Control Conf., 2003.
• [3] Hunnekens B G B, Heertjes M, van de Wouw N, Nijmeijer H. Performance optimization of piecewise affine variable-gain controllers for linear motion systems, Mechatronics, vol. 24, no. 6, pp. 648–660, Sep. 2014.
• [4] Armstrong B, Neevel D, Kusik T. New results in NPID control: Tracking, integral control, friction compensation and experimental results, IEEE Trans. Contr. Syst. Technol., vol. 9, pp. 399–406, Mar. 2001.
• [5] Hunnekens B G B, Heertjes M, van de Wouw N, Nijmeijer H. Synthesis of variable gain integral controllers for linear motion systems, IEEE Trans. on Contr. Syst. Technology, 23(1), pp. 139-149, 2015.
• [6] Armstrong B., McPherson J., and Li Y. Stability of nonlinear PD control, Appl. Math. Comput. Sci., vol. 7, no. 2, pp. 101–120, 1997.
• [7] Armstrong B., Neevel D., and Kusik T. New results in NPID control: Tracking, integral control, friction compensation and experimental results, in Proc. 1999 Int. Conf. Robot. Automat., 1999, pp. 837–842.
• [8] Armstrong B. and Wade B. Nonlinear PID control with partial state knowledge: Damping without derivatives, Int. J. Robot. Res., vol. 18, no. 8, pp. 715–731, 2000.
• [9] Armstrong B, Neevel D, Kusik T. New results in NPID control: Tracking, integral control, friction compensation and experimental results, IEEE Trans. Control Syst. Technol., vol. 9, no. 2, pp. 399–406, Mar. 2001.
• [10] Heertjes M, Schuurbiers X, Nijmeijer H. Performance-improved design of N-PID controlled motion systems with application to wafer stages, IEEE Trans. Ind. Electron., vol. 56, no. 5, pp. 1347–1355, May 2009.
• [11] Wouw N, Pastink H, Heertjes M, Pavlov A, Nijmeijer H. Performance of convergence-based variable-gain control of optical storage drives, Automatica, vol. 44, no. 1, pp. 15–27, 2008.
• [12] Sun D, Hu S, Shao X, Liu C. Global stability of a saturated nonlinear PID controller for robot manipulators, IEEE Trans. Ind. Electron., vol. 17, no. 4, pp. 892–899, Jul. 2009.
• [13] Salim S N S, Rahmat M F, Faudzi A A, Athif M, Ismail Z H, Sunar N. Position Control of Pneumatic Actuator Using Self-Regulation Nonlinear PID, Mathematical Problems in Engineering, vol. 2014, p. 12, 2014
• [14] Seraji H. A new class of nonlinear PID controllers with robotic applications, J. Robot. Syst., vol. 15, no. 3, pp. 161–173, 1998.
• [15] Su Y X, Sun D, Duan B Y. Design of an enhanced nonlinear PID controller, Mechatronics, vol. 15, no. 8, pp. 1005–1024, Oct. 2005.
• [16] Salim S N S, Rahmat M F, Faudzi A, Z. Ismail Z H, Sunar N. Robust Control Strategy for Pneumatic Drive System via Enhanced Nonlinear PID Controller, International Journal of Electrical and Computer Engineering (IJECE), vol. 4, pp. 658-667, 2014.
• [17] Armstrong B, McPherson J, Li YG. A Lyapunov stability proof for nonlinear stiffness PD control, Proceedings of the IEEE international conference on robot. autom., Minneapolis, p. 945–50, 1996.
• [18] Xu Y, Ma D, Hollerbach J. M. Nonlinear Proportional and Derivative Control for High Disturbance Rejection and High Gain Force Control, Proc. IEEE Intern. Conf. on Robotics and Automation, Vol. 1, pp. 752-759, Atlanta, 1993.
• [19] Tan, N, Kaya, I, Yeroglu C, Atherton, D. P. Computation of stabilizing PI and PID controllers using the stability boundary locus. Energy Conversion and Management, 47(18), 3045-3058.
• [20] Yeroglu C, Tan N. Design of robust PI controller for vehicle suspension system. Journal of Electrical Engineering and Technology, 3(1), 135-142.
• [21] Khalil H K, Grizzle J. Nonlinear Systems, 3rd ed. Englewood Cliffs, NJ, USA: Prentice-Hall, 2002.
• [22] Active suspension system - Laboratory Guide, Active Suspension Experiment for Matlab/Simulink Users, 2013.
Subjects Engineering Articles Orcid: 0000-0003-2782-5566Author: Ali Fuat ErgencCountry: Turkey Author: Handan NakInstitution: İSTANBUL TEKNİK ÜNİVERSİTESİCountry: Turkey Author: Şirin AkkayaInstitution: İSTANBUL TEKNİK ÜNİVERSİTESİCountry: Turkey Publication Date: October 31, 2017
 Bibtex @research article { aubtda340651, journal = {ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY A - Applied Sciences and Engineering}, issn = {1302-3160}, eissn = {2146-0205}, address = {Eskişehir Teknik Üniversitesi}, year = {2017}, volume = {18}, pages = {876 - 896}, doi = {10.18038/aubtda.340651}, title = {DESIGN, ANALYSIS AND EXPERIMENTAL VERIFICATION OF A NOVEL NONLINEAR PI CONTROLLER}, key = {cite}, author = {Ergenc, Ali Fuat and Nak, Handan and Akkaya, Şirin} } APA Ergenc, A , Nak, H , Akkaya, Ş . (2017). DESIGN, ANALYSIS AND EXPERIMENTAL VERIFICATION OF A NOVEL NONLINEAR PI CONTROLLER. ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY A - Applied Sciences and Engineering, 18 (4), 876-896. DOI: 10.18038/aubtda.340651 MLA Ergenc, A , Nak, H , Akkaya, Ş . "DESIGN, ANALYSIS AND EXPERIMENTAL VERIFICATION OF A NOVEL NONLINEAR PI CONTROLLER". ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY A - Applied Sciences and Engineering 18 (2017): 876-896 Chicago Ergenc, A , Nak, H , Akkaya, Ş . "DESIGN, ANALYSIS AND EXPERIMENTAL VERIFICATION OF A NOVEL NONLINEAR PI CONTROLLER". ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY A - Applied Sciences and Engineering 18 (2017): 876-896 RIS TY - JOUR T1 - DESIGN, ANALYSIS AND EXPERIMENTAL VERIFICATION OF A NOVEL NONLINEAR PI CONTROLLER AU - Ali Fuat Ergenc , Handan Nak , Şirin Akkaya Y1 - 2017 PY - 2017 N1 - doi: 10.18038/aubtda.340651 DO - 10.18038/aubtda.340651 T2 - ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY A - Applied Sciences and Engineering JF - Journal JO - JOR SP - 876 EP - 896 VL - 18 IS - 4 SN - 1302-3160-2146-0205 M3 - doi: 10.18038/aubtda.340651 UR - https://doi.org/10.18038/aubtda.340651 Y2 - 2017 ER - EndNote %0 ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY A - Applied Sciences and Engineering DESIGN, ANALYSIS AND EXPERIMENTAL VERIFICATION OF A NOVEL NONLINEAR PI CONTROLLER %A Ali Fuat Ergenc , Handan Nak , Şirin Akkaya %T DESIGN, ANALYSIS AND EXPERIMENTAL VERIFICATION OF A NOVEL NONLINEAR PI CONTROLLER %D 2017 %J ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY A - Applied Sciences and Engineering %P 1302-3160-2146-0205 %V 18 %N 4 %R doi: 10.18038/aubtda.340651 %U 10.18038/aubtda.340651 ISNAD Ergenc, Ali Fuat , Nak, Handan , Akkaya, Şirin . "DESIGN, ANALYSIS AND EXPERIMENTAL VERIFICATION OF A NOVEL NONLINEAR PI CONTROLLER". ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY A - Applied Sciences and Engineering 18 / 4 (October 2017): 876-896. https://doi.org/10.18038/aubtda.340651 AMA Ergenc A , Nak H , Akkaya Ş . DESIGN, ANALYSIS AND EXPERIMENTAL VERIFICATION OF A NOVEL NONLINEAR PI CONTROLLER. AUJST-A. 2017; 18(4): 876-896. Vancouver Ergenc A , Nak H , Akkaya Ş . DESIGN, ANALYSIS AND EXPERIMENTAL VERIFICATION OF A NOVEL NONLINEAR PI CONTROLLER. ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY A - Applied Sciences and Engineering. 2017; 18(4): 896-876.